Leveraged ETF Tracking Error

Dec. 15, 2018 9:09 AM ETSPY, SPXL5 Comments
David Kotok profile picture
David Kotok
2.22K Followers

By Leo Chen

We discussed the goal of leveraged ETFs previously - to provide daily returns that match the desired ratio over the underlying index (here). These ETFs rebalance daily to maintain the proportional leverage through derivatives such as futures, forwards, and swaps. We will demonstrate that this daily rebalancing feature dictates the long-term returns of leveraged ETFs, deviating from the multiple of the underlying index over the same period due to compounding.

One of our earlier commentaries compared the long-term returns of a leveraged ETF and an unleveraged index that suffers from a lack of compounding. We will revisit the issue with a simple example. If an index returned 30% in one year, then the arithmetic average daily return would be 0.1190%, using 252 trading days a year (1); however, the geometric average would be 0.1042% (2):

30%/252 ≈ 0.1190% (1)
(1+30%)1/252 - 1 ≈ 0.1042% (2)

Apparently, requiring both daily and long-term returns of leveraged ETFs to match the underlying index is not realistic. Hence, given that leveraged ETFs' target is to track the daily multiple returns, we recommend focusing on the daily tracking error.* We continue with our previous choice of the ETF, the Direxion Daily S&P 500 Bull 3x Shares ETF (SPXL), as our example. We use one of the largest ETFs, the SPDR S&P 500 Trust ETF (SPY), as our comparison. First, we notice that the correlation between SPX and SPY has been lower than the correlation between SPX and SPXL (Table 1) since their inceptions. Moreover, the average daily tracking errors of SPY and SPXL are both very small, around 0.01%. The spread between the tracking errors is only 0.0034% (Table 2), net of expenses. On the other hand, we also compare the absolute values of these daily tracking errors. Interestingly, even if both the absolute values are greater than before, the spread between the absolute

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David Kotok profile picture
2.22K Followers
David Kotok co-founded Cumberland Advisors in 1973 and has been its Chief Investment Officer since inception. David’s articles and financial market commentaries have appeared in The New York Times, The Wall Street Journal, Barron’s, and other publications. He is a frequent contributor to Bloomberg TV and Bloomberg Radio, Yahoo Finance TV, and other media. He has authored or co-authored four books, including the second edition of From Bear to Bull with ETFs and Adventures in Muniland. He holds a B.S. in economics from The Wharton School of the University of Pennsylvania, an M.S. in organizational dynamics from The School of Arts and Sciences at the University of Pennsylvania, and an M.A. in philosophy from the University of Pennsylvania.David has served as Program Chairman and currently serves as a Director of the Global Interdependence Center (GIC), www.interdependence.org, whose mission is to encourage the expansion of global dialogue and free trade in order to improve cooperation and understanding among nation states, with the goal of reducing international conflicts and improving worldwide living standards. David chaired its Central Banking Series and organized a five-continent dialogue held in Cape Town, Hong Kong, Hanoi, Milan, Paris, Philadelphia, Prague, Rome, Santiago, Shanghai, Singapore, Tallinn, and Zambia (Livingstone). He has received the Global Citizen Award from GIC for his efforts. David is a member of the National Business Economics Issues Council (NBEIC), the National Association for Business Economics (NABE), has served on the Research Advisory Board of BCA Research and is currently on the advisory board of RiskBridge Advisors. He has also served as a Commissioner of the Delaware River Port Authority (DRPA) and on the Treasury Transition Teams for New Jersey Governors Kean and Whitman. Additionally, he has served as a board member of the New Jersey Economic Development Authority and as Chairman of the New Jersey Casino Reinvestment Development Authority.

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